Complex Numbers · NDA previous year questions

2014 9 questions

1. Q52014 · 28 Sept 2014

   Let z be a complex number such that $|z|=4$ and $\arg z=\frac{5\pi }{6}$. What is z equal to ? where $i=\sqrt{-1}$

   1. A.$2\sqrt{3}+2i$
   2. B.$2\sqrt{3}-2i$
   3. C.$-2\sqrt{3}+2i$
   4. D.$-\sqrt{3}+i$
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   Answer: C

2. Q72014 · 20 Apr 2014

   If $P$ and $Q$ are two complex numbers, then the modulus of the quotient of $P$ and $Q$ is:

   1. A.Greater than the quotient of their moduli
   2. B.Less than the quotient of their moduli
   3. C.Less than or equal to the quotient of their moduli
   4. D.Equal to the quotient of their moduli
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   Answer: D

3. Q102014 · 20 Apr 2014

   What is the argument of the complex number $\frac{(1+i)(2+i)}{3-i}$ where $i=\sqrt{-1}$?

   1. A.0
   2. B.$\frac{\pi }{4}$
   3. C.$-\frac{\pi }{4}$
   4. D.$\frac{\pi }{2}$
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   Answer: D

4. Q142014 · 20 Apr 2014

   The roots of the equation $2a^2{x}^2-2abx+b^2=0$ when $a<0$ and $b>0$ are:

   1. A.Sometimes complex
   2. B.Always irrational
   3. C.Always complex
   4. D.Always real
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   Answer: C

5. Q152014 · 20 Apr 2014

   For the next three (03) items that follow: Given that $C(n,r):C(n,r+1)=1:2$ and $C(n,r+1):C(n,r+2)=2:3$. What is $n$ equal to?

   1. A.11
   2. B.12
   3. C.13
   4. D.14
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   Answer: D

6. Q162014 · 20 Apr 2014

   For the next three (03) items that follow: Given that $C(n,r):C(n,r+1)=1:2$ and $C(n,r+1):C(n,r+2)=2:3$. What is $r$ equal to?

   1. A.2
   2. B.3
   3. C.4
   4. D.5
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   Answer: C

7. Q172014 · 20 Apr 2014

   For the next three (03) items that follow: Given that $C(n,r):C(n,r+1)=1:2$ and $C(n,r+1):C(n,r+2)=2:3$. What is $P(n,r):C(n,r)$ equal to?

   1. A.6
   2. B.24
   3. C.120
   4. D.720
   Show answer

   Answer: B

8. Q182014 · 20 Apr 2014

   Out of 7 consonants and 4 vowels, words are to be formed by involving 3 consonants and 2 vowels. The number of such words formed is:

   1. A.25200
   2. B.22500
   3. C.10080
   4. D.5040
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   Answer: A

9. Q192014 · 20 Apr 2014

   How many different words can be formed by taking four letters out of the letters of the word ‘AGAIN’ if each word has to start with A?

   1. A.6
   2. B.12
   3. C.24
   4. D.None of the above
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   Answer: C